bioRxiv preprint doi: https://doi.org/10.1101/849711; this version posted November 21, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. Controlling spatiotemporal pattern formation in a concentration gradient with a synthetic toggle switch Içvara Barbier1, Rubén Perez Carrasco2* and Yolanda Schaerli1* 1 Department of Fundamental Microbiology, University of Lausanne, Biophore Building, 1015 Lausanne, Switzerland 2 Department of Mathematics, University College London, Gower Street, WC1E 6BT London, United Kingdom *Correspondence: [email protected] and [email protected] Abstract The formation of spatiotemporal patterns of gene expression is frequently guided by gradients of diffusible signaling molecules. The toggle switch subnetwork, composed of two cross-repressing transcription factors, is a common component of gene regulatory networks in charge of patterning, converting the continuous information provided by the gradient into discrete abutting stripes of gene expression. We present a synthetic biology framework to understand and characterize the spatiotemporal patterning properties of the toggle switch. To this end, we built a synthetic toggle switch controllable by diffusible molecules in Escherichia coli. We analyzed the patterning capabilities of the circuit by combining quantitative measurements with a mathematical reconstruction of the underlying dynamical system. The toggle switch can produce robust patterns with sharp boundaries, governed by bistability and hysteresis. We further demonstrate how the hysteresis, position, timing, and precision of the boundary can be controlled, highlighting the dynamical flexibility of the circuit. Keywords: Synthetic biology, gene regulatory networks, pattern formation, dynamical systems, bistability, hysteresis 1 bioRxiv preprint doi: https://doi.org/10.1101/849711; this version posted November 21, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. Introduction Synthetic biology aims to engineer living organisms with standardized and modular circuits that perform their functions in a programmable and predictable way (Brophy and Voigt, 2014, Cameron et al., 2014, Purcell and Lu, 2014). In addition to the promise of providing new technologies for medical and industrial applications (Gilbert and Ellis, 2018, Kitada et al., 2018, Nielsen and Keasling, 2016, Xie and Fussenegger, 2018), recapitulating biological processes synthetically provides a route to understanding the basic necessary mechanisms underpinning biological functions and dissect their properties and limitations (Bashor and Collins, 2018, Li et al., 2018). Formation of spatiotemporal patterns of gene expression, a crucial process during the development of multicellular organisms, lends itself to be studied by such a synthetic biology approach. During development, pattern formation is achieved through a set of inter-connected gene regulatory programs encoding different non-linear responses to spatial chemical cues. This multiscale complexity makes the elucidation of the core principles of spatial patterning very challenging in living embryos, calling for alternative approaches capable of interrogating and comparing different pattern formation mechanisms. The rise of synthetic biology has successfully allowed to build synthetic systems able to explore core patterning principles (reviewed in (Santos-Moreno and Schaerli, 2019b, Luo et al., 2019, Davies, 2017, Ebrahimkhani and Ebisuya, 2019)). In addition, synthetic pattern formation is also an attractive technology for the engineering of living materials (Gilbert and Ellis, 2018, Nguyen et al., 2018, Moser et al., 2019, Cao et al., 2017) and tissues (Davies and Cachat, 2016, Healy and Deans, 2019, Webster et al., 2016). One ubiquitous strategy of patterning during embryogenesis is positional information, in which signaling molecules – the morphogens – diffuse and generate concentration gradients to specify positions. Specific gene regulatory programs are able to translate the spatiotemporal information provided by the local concentration of morphogen gradients into robust gene expression patterns (Wolpert, 1996, Green and Sharpe, 2015, Rogers and Schier, 2011). This mechanism has been extensively used in synthetic systems to generate spatial patterns, especially stripe patterns, which were produced through synthetic feed-forward loops (Basu et al., 2005, Schaerli et al., 2014), inducible promoters (Grant et al., 2016) and AND-gates (Boehm et al., 2018). One of the gene regulatory subnetworks able of interpreting positional information is the bistable genetic switch (Zhang et al., 2012, Srinivasan et al., 2014, Balaskas et al., 2012, Kraut and Levine, 1991, Lopes et al., 2008b, Perez-Carrasco et al., 2016, Sokolowski et al., 2012, Zagorski et al., 2017, Alon, 2007), known as toggle switch (TS) (Figure 1A). The topology of this circuit consists of two cross-repressing nodes that result in the binary mutually exclusive stable expression of one of the nodes. If the expression is influenced by an external signal, the TS provides a mechanism to convert a concentration gradient of this signal into stripes of gene expression (Perez-Carrasco et al., 2016, Sokolowski et al., 2012). Examples of TS-controlled pattern formation have been identified in the mesoderm formation in Xenopus (Saka and Smith, 2007), Drosophila blastoderm gap gene segmentation (Verd et al., 2019, Clark, 2017), 2 bioRxiv preprint doi: https://doi.org/10.1101/849711; this version posted November 21, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. and neural specification in vertebrate neural tube (Briscoe and Small, 2015, Perez-Carrasco et al., 2018). The non-linearity of gene regulatory networks such as the TS impedes to intuitively understand the effect that different kinetic parameters have on the dynamics of gene expression. For this reason, during the last decade, gene regulatory networks have been analyzed using tools from dynamical systems theory, associating the stable steady states of the dynamical system with the attainable gene expression states of a cell. Similarly, the change in the availability of cellular states as a consequence of perturbations of kinetic parameters of the network can be associated with the bifurcations of the dynamical system, providing information of the constraints of the possible cellular states. Indeed, the dynamical system of the TS has been thoroughly analyzed in silico, both in single cells as well as in population-level patterning scenarios (Perez-Carrasco et al., 2016, Ferrell, 2002, Guantes and Poyatos, 2008), showing that two possible stable states can coexist for a region of parameters inside which the expression state of the cell will depend on the initial gene expression – a phenomenon known as bistability. Under the control of an external signal, this bistability leads to hysteresis in which the state of the system is robust to signal changes, thus providing memory to gene expression patterns (Wang et al., 2009). Interestingly, the analysis of the steady states of the dynamical system not only provides static information of the cellular states, but also information on the transient dynamics of gene expression by which the states are attained (Verd et al., 2014). Therefore, a map of the underlying dynamical system is critical to fully understand the dynamics of the TS network. The first synthetic version of the TS network was built almost 20 years ago and was a milestone of synthetic biology (Gardner et al., 2000). Since then, it has been built multiple times, extensively studied and used for its memory, bistability or hysteresis properties (Padirac et al., 2012, Purcell and Lu, 2014, Chen and Arkin, 2012, Lou et al., 2010, Andrews et al., 2018, Yang et al., 2019, Nikolaev and Sontag, 2016, Zhao et al., 2015, Sokolowski et al., 2012, Lebar et al., 2014), for stochasticity fate choice (Axelrod et al., 2015, Perez-Carrasco et al., 2016, Sekine et al., 2011, Wu et al., 2013, Lugagne et al., 2017) and to tune threshold activation (Gao et al., 2018). Nevertheless, its patterning capabilities controlled with a morphogen-like signal have not been studied in a synthetic system. Here, we constructed a “morphogen”-inducible synthetic TS network and studied its ability to produce spatial patterns - governed by bistability and hysteresis - in an Escherichia coli (E. coli) population. A combination of experiments and mathematical modelling allowed us to characterize the underlying bifurcation diagram, unveiling the possible dynamical regimes of the circuit. This enabled us to demonstrate how the inducible TS allows to control hysteresis, precision, position and timing of the pattern boundary. 3 bioRxiv preprint doi: https://doi.org/10.1101/849711; this version posted November 21, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC